Let \(G \,=\,\mathrm {SU}(2)\) . The extended moduli space [1]} for a genus \(g\)  surface \(\Sigma _g\)  with one boundary component was developed for the same purpose as the quasi-Hamiltonian \(G\) -space from [2]}. It has a symplectic structure and a Hamiltonian action of \(G\) . Its symplectic quotient (at a specific coadjoint orbit of \(G\) ) is the moduli space of parabolic bundles associated to that orbit. It has real dimension \(6g\) .
